Unformatted text preview: EE‐564 Fall 2009 Mock Exam Monday, September 21, 2009 1. Consider the following binary hypothesis testing problem: 4 0,2 9 : 1 3,4 9 0 2 3 0,3 : 9 0 a) Determine the associated probability of detection for the Neyman‐Pearson detector, and plot the receiver operating characteristic ( versus ) for the following two regions of : i. For 0,0.5 . ii. For 0.5,1 . (Note: It is recommended that you solve this part after you are done with the remainder of the exam.) (Hint: Plot the above pdf functions and first.) b) For the following priors and cost matrix, determine the Bayes optimal rule and the associated risk. 1 2 Prior Probabilities: , 3 3 01 40 2. Consider the following 4‐ary hypothesis testing problem with the following signals: : √2 1 √2 0 1 2 0 2 Where 3 √2 are deterministic signals and , , , 2 , is a Gaussian random process with the 0 , 1,2,3,4 , following second moment statistics: a) Sketch the constellation diagram and mark decision regions for the maximum likelihood symbol detector. b) Derive an upper and lower bound on the symbol error probability. Assume equal prior probabilities. ...
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 hypothesis testing problem, binary hypothesis testing

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